NDSolve PDE with particular variables dependence

Hi, I would ask you if (and eventually how) it is possible to numerically solve with mathematica a partial differential equation of the form:

ddd.jpg

I tried to use NDSolve but I don’t know how to manage the (y,y) dependence, indeed mathematica tell me:

NDSolve::conarg: The arguments should be ordered consistently.

Any hint would be precious, thank you!